Inorder traversal

Programs that utilize tree structures need to process nodes in a tree (represented as circles in below diagram). Nodes contain information about an object. For now, let's assume each node contains a letter. The arrows indicate a link between nodes.

Inorder Traversal is a type of tree traversal algorithm. Inorder refers to when the root is processed inbetween to its two subtrees.

Steps to Inorder Traversal

Given a non-empty tree,

1. Process the nodes in the left subtree with a recursive call
2. Process the root
3. Process the nodes in the right subtree with a recursive call

template 
int inorder_print(const binary_tree_nodes* ptr)
// ptr is a pointer to a node in a binary tree OR null
// meaning empty tree.
{
   if (ptr != NULL)
   {
       inorder_print( ptr->left() );
       std::cout << ptr->data() << std::endl;
       inorder_print( ptr->right() );
   }
   return 0;
}

data Tree a = ET | Node(a, Tree a, Tree a)

inorder :: Tree a -> [a]
inorder ET = []
inorder (Node (x, left,right)) = (inorder left) ++ [x] ++ (inorder right)